A representative of the people must vote always as they would vote. 
A Congressman is a representative of the people. 
Therefore, Congressmen must vote always as the people who elect them
    would vote.

Is not the expression, representative of the people, here used in two different senses?

When an argument is delivered, one of the premises—­being a statement which the speaker assumes everyone will admit as true—­is sometimes omitted.  This shortened form is called an enthymeme.

     Smith will be a successful civil engineer for he is a
     superior mathematician.

Supply the missing premise.  Which is it?

In the bald, simple forms here set down, the syllogism and enthymeme are hardly suited to delivery in speeches.  They must be amplified, explained, emphasized, in order to serve a real purpose.  The following represent better the way a speaker uses deductive reasoning.

The appointing power is vested in the President and Senate; this is the general rule of the Constitution.  The removing power is part of the appointing power; it cannot be separated from the rest.

     DANIEL WEBSTER:  The Appointing and Removing
     Power, 1835

Then Daniel Webster stated in rather extended form the conclusion that the Senate should share in the removing proceedings.

Sir, those who espouse the doctrines of nullification reject, as it seems to me, the first great principle of all republican liberty; that is, that the majority must govern.  In matters of common concern, the judgment of a majority must stand as the judgment of the whole.

     DANIEL WEBSTER:  Reply to Calhoun, 1853

Then, he argues, as these revenue laws were passed by a majority, they must be obeyed in South Carolina.

Methods of Proof.  In extended arguments, just as in detailed exposition, many different methods of proof may be employed.

Explanation.  Often a mere clear explanation will induce a listener to accept your view of the truth of a proposition.  You have heard men say, “Oh, if that is what you mean, I agree with you entirely.  I simply didn’t understand you.”  When you are about to engage in argument consider this method of exposition to see if it will suffice.  In all argument there is a great deal of formal or incidental explanation.

Authority.  When authority is cited to prove a statement it must be subjected to the same tests in argument as in explanation.  Is the authority reliable?  Is he unprejudiced?  Does his testimony fit in with the circumstances under consideration?  Will his statements convince a person likely to be on the opposing side?  Why has so much so-called authoritative information concerning conditions in Europe been so discounted?  Is it not because the reporters are likely to be prejudiced and because while what they say may be true of certain places and conditions it does not apply to all the points under discussion?  The speaker who wants the support of authority will test it as carefully as though its influence is to be used against him—­as indeed, it frequently is.